4 papers
Sublattices of lattices of order-convex sets, I. The main representation theorem
Marina V. Semenova, Friedrich Wehrung
For a partially ordered set P, we denote by Co(P) the lattice of order-convex subsets of P. We find three new lattice identities, (S), (U), and (B), such that the following result…
Sublattices of lattices of order-convex sets, II. Posets of finite length
Marina V. Semenova, Friedrich Wehrung
For a positive integer n, we denote by SUB (resp., SUBn) the class of all lattices that can be embedded into the lattice Co(P) of all order-convex subsets of a partially ordered se…
Sublattices of lattices of order-convex sets, III. The case of totally ordered sets
Marina V. Semenova, Friedrich Wehrung
For a partially ordered set P, let Co(P) denote the lattice of all order-convex subsets of P. For a positive integer n, we denote by SUB(LO) (resp., SUB(n)) the class of all lattic…
Sublattices of lattices of convex subsets of vector spaces
Friedrich Wehrung, Marina V. Semenova
For a left vector space V over a totally ordered division ring F, let Co(V) denote the lattice of convex subsets of V. We prove that every lattice L can be embedded into Co(V) for…